Transcript Pindyck/Rubinfeld Microeconomics

CHAPTER
13
Game Theory and
Competitive Strategy
CHAPTER OUTLINE
13.1 Gaming and Strategic
Decisions
13.2 Dominant Strategies
13.3 The Nash Equilibrium
Revisited
13.4 Repeated Games
13.5 Sequential Games
13.6 Threats, Commitments
and Credibility
13.7 Entry Deterrence
13.8 Auctions
Prepared by:
Fernando Quijano, Illustrator
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13.1 Gaming and Strategic Decisions
● game Situation in which players (participants) make strategic
decisions that take into account each other’s actions and responses.
● payoff
● strategy
Value associated with a possible outcome.
Rule or plan of action for playing a game.
● optimal strategy
Strategy that maximizes a player’s expected payoff.
If I believe that my competitors are rational and act to maximize their own
payoffs, how should I take their behavior into account when making my
decisions?
Determining optimal strategies can be difficult, even under conditions of
complete symmetry and perfect information.
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Noncooperative versus Cooperative Games
● cooperative game Game in which participants can negotiate
binding contracts that allow them to plan joint strategies.
● noncooperative game Game in which negotiation and enforcement of
binding contracts are not possible.
It is essential to understand your opponent’s point of view and to deduce his
or her likely responses to your actions.
Note that the fundamental difference between cooperative and noncooperative
games lies in the contracting possibilities. In cooperative games, binding
contracts are possible; in noncooperative games, they are not.
HOW TO BUY A DOLLAR BILL
A dollar bill is auctioned, but in an unusual way. The highest bidder receives the
dollar in return for the amount bid. However, the second-highest bidder must
also hand over the amount that he or she bid—and get nothing in return.
If you were playing this game, how much would you bid for the dollar bill?
Classroom experience shows that students often end up bidding more than a
dollar for the dollar.
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13.2 Dominant Strategies
● dominant strategy
opponent does.
TABLE 13.1
Strategy that is optimal no matter what an
PAYOFF MATRIX FOR ADVERTISING GAME
Firm B
Firm A
Advertise
Don’t advertise
Advertise
10, 5
15, 0
Don’t advertise
6, 8
10, 2
Advertising is a dominant strategy for Firm A. The same is true for
Firm B: No matter what firm A does, Firm B does best by advertising. The
outcome for this game is that both firms will advertise.
● equilibrium in dominant strategies Outcome of a game in which each firm
is doing the best it can regardless of what its competitors are doing.
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Unfortunately, not every game has a dominant strategy for each player.
TABLE 13.2
MODIFIED ADVERTISING GAME
Firm 2
Firm 1
Advertise
Don’t advertise
Advertise
10, 5
15, 0
Don’t advertise
6, 8
20, 2
Now Firm A has no dominant strategy. Its optimal decision depends on what
Firm B does. If Firm B advertises, Firm A does best by advertising; but if Firm B
does not advertise, Firm A also does best by not advertising.
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13.3 The Nash Equilibrium Revisited
Dominant Strategies: I’m doing the best I can no matter what you do.
You’re doing the best you can no matter what I do.
Nash Equilibrium:
I’m doing the best I can given what you are doing.
You’re doing the best you can given what I am doing.
THE PRODUCT CHOICE PROBLEM
Two new variations of cereal can be successfully introduced—provided that
each variation is introduced by only one firm.
TABLE 13.3
PRODUCT CHOICE PROBLEM
Firm 2
Firm 1
Crispy
Sweet
Crispy
–5, –5
10, 10
Sweet
10, 10
–5, –5
In this game, each firm is indifferent about which product it produces—so long as it does
not introduce the same product as its competitor. The strategy set given by the bottom lefthand corner of the payoff matrix is stable and constitutes a Nash equilibrium: Given the
strategy of its opponent, each firm is doing the best it can and has no incentive to deviate.
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Maximin Strategies
TABLE 13.4
MAXIMIN STRATEGY
Firm 2
Firm 1
Don’t invest
Invest
Don’t invest
Invest
0, 0
–10, 10
–100, 0
20, 10
In this game, the outcome (invest, invest) is a Nash equilibrium. But if
you are concerned that the managers of Firm 2 might not be fully informed or
rational—you might choose to play “don’t invest.” In that case, the worst that
can happen is that you will lose $10 million; you no longer have a chance of
losing $100 million.
● maximin strategy
earned.
Strategy that maximizes the minimum gain that can be
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THE PRISONERS’ DILEMMA
TABLE 13.5
PRISONERS’ DILEMMA
Prisoner B
Prisoner A
Confess
Don’t confess
Confess
–5, –5
–1, –10
Don’t confess
–10, –1
–2, –2
the ideal outcome is one in which neither prisoner
confesses, so that both get two years in prison. Confessing, however, is a
dominant strategy for each prisoner—it yields a higher payoff regardless of the
strategy of the other prisoner.
Dominant strategies are also maximin strategies. The outcome in which both
prisoners confess is both a Nash equilibrium and a maximin solution. Thus, in a
very strong sense, it is rational for each prisoner to confess.
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13.4 Repeated Games
● repeated game Game in which actions are taken and payoffs
received over and over again.
TABLE 13.8
PRICING PROBLEM
Firm 2
Firm 1
Low price
High price
Low price
10, 10
100, –50
High price
–50, 100
50, 50
Suppose this game is repeated over and over again—for example, you and
your competitor simultaneously announce your prices on the first day of every
month. Should you then play the game differently?
TIT-FOR-TAT STRATEGY
In the pricing problem above, the repeated game strategy that works best is the
tit-for-tat strategy.
● tit-for-tat strategy Repeated-game strategy in which a player responds in
kind to an opponent’s previous play, cooperating with cooperative opponents
and retaliating against uncooperative ones.
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INFINITELY REPEATED GAME
When my competitor and I repeatedly set prices month after month,
forever, cooperative behavior (i.e., charging a high price) is then the
rational response to a tit-for-tat strategy. (This assumes that my competitor
knows, or can figure out, that I am using a tit-for-tat strategy.) It is not rational to
undercut.
With infinite repetition of the game, the expected gains from cooperation will
outweigh those from undercutting. This will be true even if the probability that I
am playing tit-for-tat (and so will continue cooperating) is small.
FINITE NUMBER OF REPETITIONS
Now suppose the game is repeated a finite number of times—say, N months. (N
can be large as long as it is finite.) If my competitor (Firm 2) is rational and
believes that I am rational.
In this case, both firms will not consider undercutting until the last month, before
the game is over, so Firm 1 cannot retaliate.
However, Firm 2 knows that I will charge a low price in the last month. But then
what about the next-to-last month? Because there will be no cooperation in the
last month, anyway, Firm 2 figures that it should undercut and charge a low price
in the next-to-last month. But, of course, I have figured this out too. In the end,
the only rational outcome is for both of us to charge a low price every month.
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TIT-FOR-TAT IN PRACTICE
The tit-for-tat strategy can sometimes work and cooperation can
prevail. There are two primary reasons.
First, most managers don’t know how long they will be competing with their rivals.
The unraveling argument that begins with a clear expectation of undercutting in the
last month no longer applies. As with an infinitely repeated game, it will be rational
to play tit-for-tat.
Second, my competitor might have some doubt about the extent of my rationality.
“Perhaps,” thinks my competitor, “Firm 1 will play tit-for-tat blindly, charging a high
price as long as I charge a high price.”
Just the possibility can make cooperative behavior a good strategy (until near the
end) if the time horizon is long enough. Although my competitor’s conjecture about
how I am playing the game might be wrong, cooperative behavior is profitable in
expected value terms. With a long time horizon, the sum of current and future
profits, weighted by the probability that the conjecture is correct, can exceed the
sum of profits from price competition, even if my competitor is the first to undercut.
Thus, in a repeated game, the prisoners’ dilemma can have a cooperative outcome.
Sometimes cooperation breaks down or never begins because there are too many
firms. More often, failure to cooperate is the result of rapidly shifting demand or cost
conditions.
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EXAMPLE 13.1
ACQUIRING A COMPANY
You represent Company A, which is considering acquiring Company T. You plan
to offer cash for all of Company T’s shares, but you are unsure what price to
offer. The value of Company T depends on the outcome of a major oil
exploration project.
If the project succeeds, Company T’s value under current management could be
as high as $100/share. Company T will be worth 50 percent more under the
management of Company A. If the project fails, Company T is worth $0/share
under either management. This offer must be made now—before the outcome
of the exploration project is known.
You (Company A) will not know the results of the exploration project when
submitting your price offer, but Company T will know the results when deciding
whether to accept your offer. Also, Company T will accept any offer by Company
A that is greater than the (per share) value of the company under current
management.
You are considering price offers in the range $0/share (i.e., making no offer at all)
to $150/share. What price per share should you offer for Company T’s stock?
The typical response—to offer between $50 and $75 per share—is wrong. The
answer is provided later in this chapter, but we urge you to try to find the answer
on your own.
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Copyright © 2013 Pearson Education, Inc. • Microeconomics • Pindyck/Rubinfeld, 8e.
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